Alone in a Cave...
Shimmy around that cliff face and into cave #2
Fashion the rope and the bedroll into a parachute and gracefully float down to the dog and mouse.
Use the rope as a leash and bring the dog with you.
Make a leash for yourself out of the rope and present it to Dog and Mouse for they are superior beings than you.
Collect the hard hat from the construction-worker zombie. It might have a mining light on it that you can use to explore deeper into the cave.
Climb down, make friends with dog, check zombies for goods, and continue following father's footsteps